# Feature Importance: A Closer Look at Shapley Values and LOCO arXiv: https://arxiv.org/abs/2303.05981 ยท HTML: https://mlsanity.com/paper/2303.05981/ ## Key facts - Cited by 23 papers in the map (data through 14 Oct 2026). - Builds on 16 of its 28 references that are in the map. - First posted on arXiv 10 Mar 2023. ## Builds on (most cited first, 16 of 16) - [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017) - [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016) - [Model-Agnostic Interpretability of Machine Learning](https://mlsanity.com/paper/1606.05386/) (2016) - [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020) - [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020) - [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022) - [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014) - [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019) - [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020) - [Floodgate: inference for model-free variable importance](https://mlsanity.com/paper/2007.01283/) (2020) - [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021) - [Decorrelated Variable Importance](https://mlsanity.com/paper/2111.10853/) (2021) - [Understanding Global Feature Contributions With Additive Importance Measures](https://mlsanity.com/paper/2004.00668/) (2020) - [MDA for random forests: inconsistency, and a practical solution via the Sobol-MDA](https://mlsanity.com/paper/2102.13347/) (2021) - [The HulC: Confidence Regions from Convex Hulls](https://mlsanity.com/paper/2105.14577/) (2021) - [Variable importance without impossible data](https://mlsanity.com/paper/2205.15750/) (2022) ## Built on by (most cited first, 23 of 23) - [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023) - [Statistical Significance of Feature Importance Rankings](https://mlsanity.com/paper/2401.15800/) (2024) - [Explainable artificial intelligence approaches for brain-computer interfaces: a review and design space](https://mlsanity.com/paper/2312.13033/) (2023) - [Precise Model Benchmarking with Only a Few Observations](https://mlsanity.com/paper/2410.05222/) (2024) - [ExplainerPFN: Towards tabular foundation models for model-free zero-shot feature importance estimations](https://mlsanity.com/paper/2601.23068/) (2026) - [I Bet You Did Not Mean That: Testing Semantic Importance via Betting](https://mlsanity.com/paper/2405.19146/) (2024) - [Measuring Variable Importance in Heterogeneous Treatment Effects with Confidence](https://mlsanity.com/paper/2408.13002/) (2024) - [Beyond Shapley Values: Cooperative Games for the Interpretation of Machine Learning Models](https://mlsanity.com/paper/2506.13900/) (2025) - [Doctor Rashomon and the UNIVERSE of Madness: Variable Importance with Unobserved Confounding and the Rashomon Effect](https://mlsanity.com/paper/2510.12734/) (2025) - [Factor Importance Ranking and Selection using Total Indices](https://mlsanity.com/paper/2401.00800/) (2024) - [Inference on Variable Importance for Treatment Effect Heterogeneity: Shapley Values and Beyond](https://mlsanity.com/paper/2510.18843/) (2025) - [Energy-Based Model for Accurate Estimation of Shapley Values in Feature Attribution](https://mlsanity.com/paper/2404.01078/) (2024) - [How to safely discard features based on aggregate SHAP values](https://mlsanity.com/paper/2503.23111/) (2025) - [Feature Attribution from First Principles](https://mlsanity.com/paper/2505.24729/) (2025) - [Regional Explanations: Bridging Local and Global Variable Importance](https://mlsanity.com/paper/2604.11223/) (2026) - [A new paradigm for global sensitivity analysis](https://mlsanity.com/paper/2409.06271/) (2024) - [Targeted Learning for Variable Importance](https://mlsanity.com/paper/2411.02221/) (2024) - [AICO: Feature Significance Tests for Supervised Learning](https://mlsanity.com/paper/2506.23396/) (2025) - [Hierarchical Variable Importance with Statistical Control for Medical Data-Based Prediction](https://mlsanity.com/paper/2508.08724/) (2025) - [Mathematical Theory of Collinearity Effects on Machine Learning Variable Importance Measures](https://mlsanity.com/paper/2510.00557/) (2025) - [How important are the genes to explain the outcome - the asymmetric Shapley value as an honest importance metric for high-dimensional features](https://mlsanity.com/paper/2603.05317/) (2026) - [Attribution Upsampling should Redistribute, Not Interpolate](https://mlsanity.com/paper/2603.16067/) (2026) - [Cluster LOCO: Feature Importance For Interpreting Clusters](https://mlsanity.com/paper/2606.14592/) (2026) ## Abstract (arXiv) There is much interest lately in explainability in statistics and machine learning. One aspect of explainability is to quantify the importance of various features (or covariates). Two popular methods for defining variable importance are LOCO (Leave Out COvariates) and Shapley Values. We take a look at the properties of these methods and their advantages and disadvantages. We are particularly interested in the effect of correlation between features which can obscure interpretability. Contrary to some claims, Shapley values do not eliminate feature correlation. We critique the game theoretic axioms for Shapley values and suggest some new axioms. We propose new, more statistically oriented axioms for feature importance and some measures that satisfy these axioms. However, correcting for correlation is a Faustian bargain: removing the effect of correlation creates other forms of bias. Ultimately, we recommend a slightly modified version of LOCO. We briefly consider how to modify Shapley values to better address feature correlation.